Hi, A thought. We had a similar sounding problem with our '85 Golf. Driving along, the engine would suddenly quit. The dealership replaced all the injectors, fuel lines, both fuel pumps, and did a full tune-up. $$$. But the problem persisted.
Usually the engine would quit after driving for 15-20 minutes. After sitting a few minutes, the engine would start again and the car would drive normally for days. The fear was getting rear eneded because there was no warning when the car would suddenly stop.
Turns out the culprit was the fuel pump relay. No guarantee it's the same problem on your car, but worth a try and relatively inexpensive to test compared to letting a shop swap out fuel injection parts in a trial and error diagonsis.
The fuel pump relay is a little black box about 5 cm long plugged into your fuse box. If you don't have a Bently manual, try the following. Find the fuel pump relay by putting your hand on a relay and turn on the ignition to the run position (not start). The fuel pump will run for a second or two to pressurize the fuel lines. You'll hear a buzzing sound from the back of the car. Then the relay kicks out and the buzzing stops. You'll feel a click when the relay kicks in and cuts out. Find the fuel pump relay by trial and error. When you think you've found it, remove it and turn the key to run position again. If you don't hear the fuel pump running, you've found it.
If you can get another fuel pump relay (buy new or test using one from a wrecking yard), plug it in and see if the problem disappears.
In my case, to confirm it was the fuel pump relay, I took the cover off the relay and noted how the relay contact was positioned (closed) when the engine was running. I drove around until the engine quit. I noticed that the relay contact was open (ignition was still in the run position) so that cinched it. The original relay was 15 years old at that time. When the faulty relay opened, the fuel pump stopped and the engine starved of fuel.
After replacing the fuel pump relay in 2000, the '85 has been running fine since.
Good luck.
-Tony